To solve current design problems of long-span stay cables,this paper proposed a new design of cable-stayed bridges with carbon fiber reinforced polymer(CFRP) and steel composite stay cables.In this design,the CFRP stay cables with high strength-to-weight ratio are applied in the dead load condition,where the high strength of stay cables is needed;while the steel stay cables with high stiffness and low cost are applied in the live load condition,where the stiffness of entire bridge is concerned.The design strategies and key design parameters for the proposed cable-stayed bridges were determined and the appropriate values of key design parameters were also suggested based on a parametric study.By comparing,it can be concluded that the proposed composite cable-stayed bridges have less cable sag and lower self-weight than cable-stayed bridges with steel stay cables and meanwhile have more stiffness and lower cost than those with CFRP stay cables.It is proved in this study that the use of CFRP and steel composite stay cables in cable-stayed bridges is feasible and the proposed composite cable-stayed bridges could become an excellent alternative to cable-stayed bridges with steel or CFRP stay cables.